Given a real-valued function/such thatfx=tan2xx2-x2,   for  x>01,       for  x = 0x  cot x  ,    for  x<0where [x] is the integral part and {x} is the fractional part of x, then

We  have  limx→0+  fx=  limx→0+  tan2xx2-x2   =  limx→0+   tan2xx2=1   1Also,   limx→0-  fx  limx→0-   xcotx=cot1                           2                x→0-,  x=-1⇒x=x+1⇒x→1Also,   cot-1limx→0-  fx2  =cot-1cot1=1.Also,   tan-1  limx→0+  fx=tan-11=π4